Low-rank tensor methods for linear systems and eigenvalue problems

By Christine Tobler. 2012

54 citations recorded by the source corpus.

Subfields: Computational Mathematics, Computational Theory and Mathematics, Statistical and Nonlinear Physics

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Citations in the corpus

A literature survey of low‐rank tensor approximation techniques (2013, neutral): “mbined with QTT [161] and low-rank matrix decompositions [189]; a projection method combined with HT [16]; the conjugate gradient method, BiCGStab and other Krylov subspace methods combined with HT [169, 171,246] and low-rank matrix decompositions [32]; GMRES combined with TT [59]. When applying an ”
Multilevel preconditioning and low‐rank tensor iteration for space–time simultaneous discretizations of parabolic PDEs (2015, methodology): “The following numerical experiments are based on the publicly available htucker toolbox [41, 42] in MATLAB, which provides a representation of a tensor in the H-Tucker format, as well as the operations described earlier.”
Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 1 Low-Rank Tensor Decompositions (2016, unknown): “Figure 22 illustrates that for a 6th-order tensor, there are only two tensor networks for its representation, while for a 5th-order we have 5, and for a 10th-order tensor there are 11 possible HT architectures [158, 257].”
Decay properties for functions of matrices over $C^*$-algebras (2013, unknown): “Matrices over such algebras arise naturally in various application areas, including parametrized linear systems and eigenproblems [18,59], differential equations [25], generalized moment problems [52], control theory [16,22,23], and quantum physics [10,11,28].”
Algorithm 941 (2014, background): “…7 is concerned with elementwise multiplication, and Section 8 with the representation of linear operators on tensors in HTD. Examples for working with htucker and a list of its complete functionality can be found in the preprint [Kressner and Tobler 2012], an extended version of this manuscript.”
Adaptive low rank wavelet methods and applications to two-electron Schrödinger equations (2012, background): “, in [101, 5, 96, 140], and for eigenvalue problems in [92, 6, 74, 102, 95, 140].”